Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of firstorder, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model [4] and a model for the sedimentation of polydisperse suspensions...

In this paper, we present a high-order weighted essentially non-oscillatory (WENO) scheme, coupled with a high-order fast sweeping method, for solving a dynamic continuum model for bidirectional flow. We first review the dynamic continuum model for bi-directional flow. This model is composed of a coupled system of a conservation law and an Eikonal equation. Then we present the first-order Lax-F...

A key idea in finite difference weighted essentially non-oscillatory (WENO) schemes is a combination of lower order fluxes to obtain a higher order approximation. The choice of the weight to each candidate stencil, which is a nonlinear function of the grid values, is crucial to the success of WENO. For the system case, WENO schemes are based on local characteristic decompositions and flux split...

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed widely concerned issue of previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is rather difficult to achieve high resolutions on premise removing spurious oscillations for long-run simulations hyperbolic systems. present study, extend OP criterion W...

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discontinuous solutions. Thanks to the mesh-less property of the RBFs, the method is suitable for non uniform grids and mesh adaptation. We focus o...

In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-or...

In this short note we address the issue of numerical resolution and efficiency of high order weighted essentially nonoscillatory (WENO) schemes for computing solutions containing both discontinuities and complex solution features, through two representative numerical examples: the double Mach reflection problem and the Rayleigh–Taylor instability problem. We conclude that for such solutions wit...

The development of a Hybrid high order Eulerian-Lagrangian algorithm to simulate shock wave interactions with particles is discussed. The Hybrid high order WENO/central finite difference scheme is assessed in three-dimensional simulations, as well as the effective use of the high order polynomials and regularization techniques in the approximation to the singular source term in the advection eq...

The fifth-order accurate Weighted Essentially Nonoscillatory space discretization developed by Jiang and Shu (WENO-JS) is studied theoretically. An exact Nonlinear Spectral Method (NSM) based on an innovative yet simple methodology. NSM explains the behaviour of nonsmooth solutions because it valid for arbitrary modified wave numbers (MWN). clarifies effects time integration methods Courant num...

The WENO-NIP scheme was obtained by developing a class of L1-norm smoothness indicators based on Newton interpolation polynomial. It recovers the optimal convergence order in smooth regions regardless critical points and achieves better resolution than classical WENO-JS scheme. However, produces severe spurious oscillations when solving 1D linear advection problems with discontinuities at long ...